The Chinese government has warned Donald Trump it is “seriously concerned” after the US president-elect indicated he might jettison a four-decade understanding with Beijing unless its leaders were prepared to strike a new “deal” with his administration.

In an interview with Fox News on Sunday, the president-elect said he saw no reason why the US should continuing abiding by the “One China” policy – under which Washington does not recognise Taiwan as a sovereign state – unless Beijing was prepared to enter into some kind of bargain.

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“I don’t know why we have to be bound by a ‘One China’ policy unless we make a deal with China having to do with other things, including trade,” Trump told the channel.

Washington’s acceptance of the “One China” principle – according to which Taiwan is officially regarded as part of the same single Chinese nation as the mainland – has been a crucial part of the foundation of US-China relations since ties between the two countries were re-established by Richard Nixon and Mao Zedong in 1972.

Trump’s comments drew an angry riposte from Beijing. Geng Shuang, a spokesman for China’s foreign ministry, told reporters that bilateral ties and “the sound and steady growth of China-US relations” would be “out of the question” were Trump to turn away from the “One China” policy.

“We urge the incoming US administration and its leaders to fully recognise the sensitivity of the Taiwan question … [and] to properly deal with Taiwan-related matters in a prudent manner so as not to disrupt or damage the overall interests of the bilateral relationship,” Geng said, describing the “One China” principle as the “political bedrock” of ties between the two countries.

The question of Taiwan, which Beijing regards as a breakaway province that should one day be reunified with the mainland, was one of China’s “core interests”, the spokesman pointed out.

In a separate statement, the ministry cited Foreign Minister Wang Yi as warning during a trip to Switzerland against moves to damage the “one China” principle, having been asked by a reporter about Trump’s call with Tsai.

“China is paying close attention to developments,” Wang said. “I can clearly say that no matter whether the Tsai Ing-wen authority, any other person in the world, or any other force, if they try and damage the one China principle and harm China’s core interests, in the end they are lifting a rock only to drop it on their feet.”

Orville Schell, the head of the Centre on US-China Relations at New York’s Asia Society, said Trump’s latest comments – which the academic described as an “incredible provocation” – were the latest example of the billionaire’s contradictory moves towards China.

“He sometimes punches Beijing and he sometimes seems to reach out and hug them. The phone call to Tsai Ing-wen would be the former. Terry Branstad would be the latter. Now we have another uppercut,” he said of the Fox News interview.

“We’re being hurt very badly by China with devaluation, with taxing us heavy at the borders when we don’t tax them, with building a massive fortress in the middle of the South China Sea, which they shouldn’t be doing, and frankly with not helping us at all with North Korea,” he told Fox News.

“You have North Korea. You have nuclear weapons and China could solve that problem and they’re not helping us at all.”

Nick Bisley, an international relations expert from La Trobe University in Melbourne, said: “The signal Trump is sending to China is: ‘You are not going to push us around; you are not going to dictate terms; we are going to be the ones who dictate terms to you’. And he’s also signalling, whether deliberately or not, that there are no sacred cows in US foreign policy, whether in Asia or anywhere else.”

Bisley said Trump’s early moves would have China’s leaders, who had anticipated dealing with a predictable “Obama 3.0” under a Clinton administration, scratching their heads.

“I think they will be genuinely befuddled and just thinking: ‘How do we deal with this guy? What’s the playbook?’” he said. “The overall consequence of all of this is that it’s going to make the region a lot more uncertain and the temperature is going to be a lot higher.”

Li Yonghui, the head of the school of international relations at the Beijing Foreign Studies University, said Trump was “testing the water” with China before taking office next month.

“It fits with the logic of a businessman. But on this issue, he has really gone off in the wrong direction. If he doesn’t understand the nature of the Taiwan issue then sooner or later he will. Taiwan is not like other issues … China will not compromise on the Taiwan issue.

“If the US wants to change the ‘One-China’ policy, then it will shake the foundations of Sino-US relations. [The consequences] are hard to imagine,” the Chinese academic warned.

In an editorial, the Global Times, a fervently nationalistic party-run tabloid, said Trump was “as ignorant as a child” in the field of diplomacy and warned him the “one China” policy was “not for sale”.

The newspaper claimed Trump’s inexperience meant he was easily “influenced or even manipulated by hardliners around him”.

It said China needed “to launch a resolute struggle with him” and should be “prepared to accompany Trump on a rollercoaster ride” for Sino-US relations. “We must buckle up, as should others around the world,” it said.

Schell said it was hard to predict how Beijing might respond to Trump’s latest gambit.

“I don’t know what Beijing is going to make of this because they have always dealt with these very square, proper people like Obama and Hillary Clinton who have always sought to keep the US policy relatively constant. And here you have someone who is doing the absolute opposite,” he said.

“I think they will be very careful about responding because in a certain sense they are meeting a brinksman just like themselves … [and] I don’t know what a brinksman or a bully does when they meet another brinksman and a bully. [Violence] would be one option, but very often one of them backs down.”